Birthday colloquium on the occasion of the 85th birthday of
Prof. em. Dr. Tammo tom Dieck
June 29th, 2023
3:30 p.m., Schlauch: Coffee and tea
4:15 p.m., Sitzungszimmer: Lecture by Prof. Dr. Wolfgang Lueck (Bonn)
Title: The Farrell-Jones Conjecture for the Hecke algebras of reductive p-adic groups
Abstract: We formulate and sketch the proof of the K-theoretic Farrell-Jones Conjecture for the Hecke algebras of reductive p-adic groups. This is the first time that a version of the farrell-Jones Conjecture for topological groups is formulated. It implies that the reductive projective class group of the Hecke algebra of a reductive p-adic group is the colimit of these for all compact open subgroups. This has been proved rationally by Bernstein and Dat using representation theory. The main applications of our result will concern the theory of smooth representations In particular we will prove a conjecture of Dat.
Most of the talk will be devoted to an introduction to the Farrell-Jones Conjecture and the theory of smooth representations of reductive p-adic groups, and discussion of applications.
This is a joint project with Arthur Bartels.
Afterwards there will be a joint dinner